Is the remembrance "Astaghfirullah Al-Atheem Allathee La Ilaha Illa Huwal-Hayyul-Qayyum wa Atubu Ilaih" (I seek forgiveness from Allah, the Magnificent, whom there is no god but He, the Ever-Living, the Sustainer, and I repent to Him) after every prayer considered an innovation (bid'ah), and what are the proofs for that?

This remembrance (dhikr) is authentically reported from the Messenger of Allah, may Allah bless him and grant him peace, and performing it after the prayer is not an innovation (bid'ah); rather, it is a supplication (du'a), and supplication after prayer is desirable. Supplication is commanded generally and specifically during times of responsiveness, including immediately after the prescribed prayers. The least that can be said about the aforementioned hadith is that it represents a form of supplication reported from him, may Allah bless him and grant him peace, and the time after the salutation of the prayer is one of the times for supplication. The reported supplication for forgiveness immediately after the salutation is: "Astaghfirullah" (I seek forgiveness from Allah) three times, and limiting oneself to this in that particular instance is more appropriate.